Cremona's table of elliptic curves

3312 = 2⁴ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 23+	Signs for the Atkin-Lehner involutions
Class	3312b	Isogeny class
Conductor	3312	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-347680512 = -1 · 28 · 310 · 23	Discriminant
Eigenvalues	2+ 3-  2  4  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39,902]	[a1,a2,a3,a4,a6]
j	-35152/1863	j-invariant
L	2.8249875775606	L(r)(E,1)/r!
Ω	1.4124937887803	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1656c1 13248bh1 1104a1 82800bq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	2	4	0	-2	2	4	+	2	8	2	-10	4	0	-6	12	2	12	-16	10	4	0	-6	-14

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Quadratic twists for elliptic curve 3312b1

-4	8	-3	5	-23
1656c1	13248bh1	1104a1	82800bq1	76176y1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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